Aims. We quantitatively studied the X-ray cluster morphology, and then investigated the relationships between the cluster X-ray morphology and various cluster characteristics determined from the optical data. Methods. Using a sample of 101 clusters at redshift z ∼ 0.05-1 taken from the Chandra archive, the X-ray morphology is characterized by a series of objectively-measured simple statistics of X-ray surface brightness, which are designed to be robust against variations of image quality caused by various exposure times and various cluster redshifts. Results. The main conclusions from this work are: (1) X-ray morphologies of clusters show no significant correlation with optical richness, or related quantities. (2) X-ray morphologies of clusters are significantly correlated with the degree to which the brightest cluster member stands out against the cluster background. (3) X-ray morphologies of clusters are also correlated with optical concentration defined by galaxy distribution including fainter populations. (4) The ratio of the strong-lensing to X-ray mass measurements is correlated with the X-ray concentration, in that highly X-ray concentrated clusters show compatible strong-lensing and X-ray mass measurements, while those with low X-ray concentration show discrepancy between the two mass measurements.
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